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Properties

Label 2667.2.bo
Level $2667$
Weight $2$
Character orbit 2667.bo
Rep. character $\chi_{2667}(64,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $768$
Sturm bound $682$

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Defining parameters

Level: \( N \) \(=\) \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2667.bo (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 127 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(682\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2667, [\chi])\).

Total New Old
Modular forms 2064 768 1296
Cusp forms 2016 768 1248
Eisenstein series 48 0 48

Trace form

\( 768 q - 10 q^{2} - 138 q^{4} + 4 q^{7} - 2 q^{8} - 128 q^{9} + O(q^{10}) \) \( 768 q - 10 q^{2} - 138 q^{4} + 4 q^{7} - 2 q^{8} - 128 q^{9} + 16 q^{10} + 16 q^{11} - 40 q^{12} + 16 q^{13} - 10 q^{14} + 8 q^{15} - 114 q^{16} + 16 q^{17} + 4 q^{18} + 16 q^{19} + 24 q^{22} + 4 q^{23} - 140 q^{25} - 44 q^{28} + 32 q^{29} + 16 q^{30} + 16 q^{31} + 34 q^{32} + 16 q^{33} + 20 q^{34} + 8 q^{35} - 124 q^{36} + 32 q^{37} - 120 q^{38} + 16 q^{39} + 104 q^{40} + 8 q^{41} + 52 q^{43} + 156 q^{44} - 32 q^{46} + 72 q^{47} - 160 q^{48} - 128 q^{49} + 116 q^{50} + 24 q^{51} - 232 q^{52} + 32 q^{53} - 20 q^{55} + 8 q^{56} + 24 q^{57} + 64 q^{58} + 72 q^{59} - 80 q^{60} - 84 q^{61} + 68 q^{62} + 4 q^{63} - 142 q^{64} - 16 q^{65} + 8 q^{66} + 112 q^{67} - 104 q^{68} + 8 q^{69} - 36 q^{71} - 2 q^{72} - 24 q^{73} - 30 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{77} + 8 q^{78} - 60 q^{79} - 60 q^{80} - 128 q^{81} + 160 q^{82} - 60 q^{83} - 32 q^{85} - 136 q^{86} + 56 q^{87} - 58 q^{88} - 4 q^{89} - 96 q^{90} + 16 q^{91} + 186 q^{92} - 32 q^{93} + 96 q^{94} + 24 q^{95} + 64 q^{97} + 4 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2667, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2667, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2667, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(127, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(381, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(889, [\chi])\)\(^{\oplus 2}\)